Elemental T and Y Shapes of Tree Networks of Ducts with Various Cross-Sectional Shapes
Publication: Journal of Hydraulic Engineering
Volume 135, Issue 2
Abstract
This paper reports optimal bifurcation shapes (T and Y) in turbulent regime of tree-shaped flows. Unlike earlier studies of T and Y constructs, here the effect of pressure losses at the junction is taken into account, and the wall roughness and duct cross-sectional shapes are free to vary. The optimal ratio of duct cross-sectional areas (as a generalization of Murray’s law), the optimal ratio of duct lengths, and the optimal angle between the branches of the Y are presented. These optimal geometrical features are reported as functions of the flow direction (splitting flow versus merging flow), wall roughness, duct cross-sectional shape, and svelteness. The svelteness, Sv, is a global property defined as the external length scale of the flow construct divided by the internal length scale. It is shown that the effect of junction pressure losses on the optimized architecture can be neglected when is greater than approximately . Two dimensionless terms are introduced and shown to be useful for the optimization of flow networks.
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Acknowledgments
J. C. Ordonez and W. Wechsatol acknowledge, with gratitude, support from the Department of Energy, the Office of Naval Research and the Thailand Research Fund.
References
American Society of Heating, Refrigerating and Air-Conditioning Engineers (ASHRAE). (1967). ASHRAE handbook of fundamentals, New York.
Azoumah, Y., Mazet, N., and Neveu, P. (2004). “Constructal network for heat and mass transfer in a solid-gas reactive porous medium.” Int. J. Heat Mass Transfer, 47, 2961–2970.
Bejan, A. (1997). Advanced engineering thermodynamics, 2nd Ed., Wiley, New York.
Bejan, A. (2000). Shape and structure, from engineering to nature, Cambridge University Press, Cambridge U.K.
Bejan, A., Dincer, I., Lorente, S., Miguel, A. F., and Reis, A. H. (2004). Porous and complex flow structures in modern technologies, Springer, New York.
Bejan, A., Lorente, S., and Wang, K. M. (2006). “Networks of channels for self-healing composite materials.” J. Appl. Phys., 100, 033528.
Bejan, A., Rocha, L. A. O., and Lorente, S. (2000). “Thermodynamic optimization of geometry: T- and Y-shaped constructs of fluid streams.” Int. J. Therm. Sci., 39, 949–960.
Chen, Y., and Cheng, P. (2002). “Heat transfer and pressure drop in fractal-like microchannel nets.” Int. J. Heat Mass Transfer, 45, 2643–2648.
Colebrook, C. F. (1938–1939 ). “Turbulent flow in pipes, with particular reference to the transition region between the smooth and rough pipe laws.” J. Inst. Civil Eng., London, 11, 133–156.
da Silva, A. K., Lorente, S., and Bejan, A. (2004). “Constructal multi-scale tree-shaped heat exchanger.” J. Appl. Phys., 96(3), 1709–1718.
Idelchik, I. E. (1986). Handbook of hydraulic resistance, 2nd Ed., Hemisphere, Washington, D.C.
Miller, D. S. (1978). Internal flow systems, BHRA Fluid Engineering, U.K.
Murray, C. D. (1926). “The physiological principle of minimal work, in the vascular system, and the cost of blood-volume.” Proc. Natl. Acad. Sci. U.S.A., 12, 207–214.
Ordonez, J. C., Bejan, A., and Cherry, R. S. (2003). “Designed porous media: Optimally nonuniform flow structures connecting one point with one or more points.” Int. J. Therm. Sci., 42, 857–870.
Poirier, H. (2003). “A theory explains the intelligence of nature.” Sci. Vie, 1034, 44–63.
Sahin, A. Z., and Kalyon, M. (2005). “Maintaining uniform surface temperature along pipes by insulation.” Energy, 30(5), 637–647.
Senn, S. M., and Poulikakos, D. (2004a). “Laminar mixing, heat transfer and pressure drop in tree-like microchannel nets and their application for thermal management in polymer electrolyte fuel cells.” J. Power Sources, 130, 178–191.
Senn, S. M., and Poulikakos, D. (2004b). “Tree networks channels as fluid distributors constructing double-starcase polymer electrolyte fuel cells.” J. Appl. Phys., 96, 842–852.
Swamee, P. K., and Jain, A. K. (1976). “Explicit equations for pipe-flow problems.” J. Hydr. Div., 102(5), 657–664.
Wechsatol, W., Lorente, S., and Bejan, A. (2001). “Tree-shaped insulated designs for the uniform distribution of hot water over an area.” Int. J. Heat Mass Transfer, 44, 311–3123.
Wechsatol, W., Lorente, S., and Bejan, A. (2002). “Optimal tree-shaped networks for fluid flow in a disc-shaped body.” Int. J. Heat Mass Transfer, 45, 4911–4924.
Wechsatol, W., Ordonez, J. C., and Kosaraju, S. C. (2006). “Constructal dendritic geometry and the existence of asymmetric bifurcation.” J. Appl. Phys., 100, 113514.
Whalley, P. B. (1987). Boiling, condensation, and gas-liquid flow, Oxford University Press, New York.
Wongwises, S. (1996). “Flooding in horizontal pipe with bend.” Int. J. Multiphase Flow, 22(1), 195–201.
Wongwises, S., and Kalinitchenko, V. A. (2002). “Mean velocity distributions in a horizontal air-water flow.” Int. J. Multiphase Flow, 28(1), 167–174.
Wood, D. J., Reddy, L. S., and Funk, J. E. (1993). “Modeling pipe networks dominated by junctions.” J. Hydraul. Eng., 119(8), 949–958.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 135 • Issue 2 • February 2009
Pages: 132 - 139
Copyright
© 2009 ASCE.
History
Received: Mar 10, 2006
Accepted: Jul 1, 2008
Published online: Feb 1, 2009
Published in print: Feb 2009
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